Advances in Complex Systems

Several recent modeling studies have attempted to understand the human immune reaction to SARS-CoV-2 infections. Such a model-based understanding provides a sound basis for fighting COVID-19 on the level of individual patients. However, in this context, a worked-out nonlinear physics analysis providing insights into underlying amplitude equations and potential COVID-19 order parameters has not been conducted so far. In order to conduct such an analysis, a three-variable virus dynamics model is considered that can account for the human immune reaction to SARS-CoV-2 infections. The model amplitudes equations are derived and the relevant order parameter is determined. In line with theoretical reasoning, it is demonstrated that the order parameter and its amplitude determine the initial stage of SARS-CoV-2 infections, in general, and the initial dynamics of immune reactions, in particular. Explicitly, this finding is demonstrated for data from four COVID-19 patients. For those patients it is also demonstrated that the remnant of the order parameter determines the final disease decline phase. In this context, a time-resolved eigenvalue analysis is conducted that reveals that the transition from the initial stage to the decline stage which is associated with a switch of the leading eigenvalue from a positive to a negative value. It is argued that the immune reaction essentially contributes to this switch. From a medical-physics point of view, this observation suggests that the immune reaction of COVID-19 patients can stabilize the virus-free fixed point of affected sites.

Due to structural heterogeneity, the main function and structure of networked systems are significantly influenced by some important nodes rather than each member. In practical, the properties of important nodes could be different from network to network, and thus a variety of algorithms have been specially designed to identify important nodes of different networks and of different dynamics. In this paper we propose a widely applicable algorithm by employing the percolation model in statistical physics, which describes the behavior of connected clusters when nodes are connected randomly. This algorithm appropriately combines the local and global properties of a network, thus it stresses the significance of nodes that neither have a visibly local importance, such as degree and clustering, nor have a visibly global importance, such as betweenness. The effectiveness of our algorithm has been illustrated in a series of networks, including model networks with different degree distributions and different degree correlations, and empirical networks. As a shell decomposition process, the framework of our algorithm has extensive application prospects in analyzing network structure, such as community, core–periphery structure, and shell structures.

The idea of discovering a few nodes with potential to impact an entire network, is known as Influence Maximization (IM) and has many real-world applications which make it one of well-studied research problems in the domain of network analysis. IM typically requires a fixed criteria of budget (number of influential nodes to be identified) as input. The fundamental premise of this research is that the budget is not the sole criteria for real-world applications. This study challenges the conventional method to identify influential nodes, and proves that it requires specification of the stoppage criteria and the model used to quantify influence. We analyze the complex interplay of various criteria that can be used to solve IM problem, and prove that changing the criterion also changes the algorithm determined as the top performer. A number of criteria are presented in this paper apart from budget, such as the spread achieved by the algorithm (in terms of number of nodes influenced) and absolute time. The proposed IMine framework provides an interface to apply influence problem on various stoppage criteria, while also providing customization option to change the model of quantifying influence spread.